Title :
Frequency cosine transform: A bridge between gradient based frequency transform and discrete cosine transform
Author :
Gu, Suicheng ; Tan, Ying ; He, Xingui
Author_Institution :
Dept. of Machine Intell., Peking Univ., Beijing
Abstract :
Discrete cosine transform(DCT) is one of the most powerful tools in image processing. In this paper, we show that each basis of the two dimensional discrete cosine transform (2D-DCT) is an ldquoeigenvectorrdquo of the frequency matrix which is used to obtain basis images of a two dimensional frequency transform (2D-FRT). We also connect the FRT and cosine transform in 1D continuous model. Then, the frequency cosine transform (FCT), is proposed based on the FRT and the DCT. The partial frequency cosine transform (PFCT) is given and discussed in details. It is shown that the FCT can be regarded as a special case of FRT or DCT and it is as sophisticated as the FRT and as fast as the DCT.
Keywords :
discrete cosine transforms; eigenvalues and eigenfunctions; gradient methods; image processing; 2D frequency transform; discrete cosine transform; eigenvector; frequency matrix; gradient based frequency transform; image processing; partial frequency cosine transform; Bridges; Discrete cosine transforms; Discrete transforms; Feature extraction; Frequency; Image processing; Machine intelligence; Matrix converters; Neural networks; Signal processing; Frequency cosine transform(FCT); Laplacian Smoothing; discrete cosine transform(DCT); feature extraction; frequency transform(FRT); image processing; local gradient;
Conference_Titel :
Neural Networks and Signal Processing, 2008 International Conference on
Conference_Location :
Nanjing
Print_ISBN :
978-1-4244-2310-1
Electronic_ISBN :
978-1-4244-2311-8
DOI :
10.1109/ICNNSP.2008.4590423
